Question

1. find (f ∘ g)(2) and (f + g)(2) when f(x) = \frac{1}{x} and g(x) = 4x + 9. (3 points)

Explanation:

Step1: Calculate $g(2)$

$g(x)=4x + 9$, so $g(2)=4\times2+9=8 + 9=17$.

Step2: Calculate $(f\circ g)(2)$

$(f\circ g)(2)=f(g(2))$. Since $g(2)=17$ and $f(x)=\frac{1}{x}$, then $f(g(2))=f(17)=\frac{1}{17}$.

Step3: Calculate $(f + g)(2)$

$(f + g)(2)=f(2)+g(2)$. First, $f(2)=\frac{1}{2}$, and $g(2)=17$. So $(f + g)(2)=\frac{1}{2}+17=\frac{1 + 34}{2}=\frac{35}{2}$.

Answer:

$(f\circ g)(2)=\frac{1}{17}$, $(f + g)(2)=\frac{35}{2}$